The value of energy in the nth orbit Let the potential energy be zero when r-0 A- n h-D-mB- n2 h2 D-2 m1-4C- n2 h2 D-2 -2 m1-4D- n h-2 -D-m

The correct option is D ∫_0^rdU=∫_0^rf.dr U(r)=Dr^2_n/2 & K=1/2mv^2_n=1/2Dr^2_n ∴ T.E=U+K=Dr^2_n = nh/2 π√(D/M) ...

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Standard IX

Chemistry

Bohr's Model of an Atom

The value of ...

Question

The value of energy in the $n^{t h}$ orbit (Let the potential energy be zero when r = 0)

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Solution

The correct option is C

$\int_{0}^{r} d U = \int_{0}^{r} \to f . \to d r U (r) = \frac{D r_{n}^{2}}{2} & K = \frac{1}{2} m v_{n}^{2} = \frac{1}{2} D r_{n}^{2} ∴ T . E = U + K = D r_{n}^{2} = \frac{n h}{2 π} \sqrt{\frac{D}{M}}$

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A particle with mass m is held in circular orbit around the origin by an attractive force F(r)=-Dr; where D is a positive constant. Assume that the Bohr model idea that ,the angular momentum is quantized i.e. it takes only integral multiples of $\frac{h}{2 π}$ holds.

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$\begin{matrix} Column I & Column II a . \frac{V_{n}}{K_{n}} = ? & p . 0 b . If radius of n^{t h} orbit \propto E_{n}^{x}, x = ? & q . - 1 c . Angular momentum in lowest orbital & r . - 2 d . \frac{1}{r_{n}} \propto Z^{y}, y = ? & s .1 \end{matrix}$

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The value of energy in the nth orbit (Let the potential energy be zero when r = 0)

The correct option is C ∫r0dU=∫r0→f.→drU(r)=Dr2n2 &K=12mv2n=12Dr2n∴T.E=U+K=Dr2n=nh2π√DM

The value of energy in the $n^{t h}$ orbit (Let the potential energy be zero when r = 0)

The correct option is C

$\int_{0}^{r} d U = \int_{0}^{r} \to f . \to d r U (r) = \frac{D r_{n}^{2}}{2} & K = \frac{1}{2} m v_{n}^{2} = \frac{1}{2} D r_{n}^{2} ∴ T . E = U + K = D r_{n}^{2} = \frac{n h}{2 π} \sqrt{\frac{D}{M}}$